Chapter 11 Estimation of Amplitude-Dependent Resonance and Damping in MEMS Shock Accelerometers Jason R. Foley, Thomas J. Lagoski, Jontia Brown, and Jonathan Hong Abstract Understanding the dynamic response of accelerometers is critical to interpreting data obtained in impulsive loading conditions. While this information is commonly provided by manufacturers, the estimated properties are typically obtained at levels below the full range of the sensor. Using high bandwidth operating data of varying amplitudes, the damping ratio and principle resonant frequency of shock accelerometers are estimated using a simple dynamic model. While the resonance is shown to be essentially amplitude-invariant, the damping ratio is shown to vary with the excitation amplitude. Possible causes related to the frequency content of the excitation and the presence of repeated roots are discussed. Keywords Shock accelerometers • Microelectromechanical systems (MEMS) • Sensors • Damping • Operating modal analysis Nomenclature Pulse width/duration ! Angular/radian frequency Phase response (frequency domain) m Mass c Damping coefficient i Imaginary number k Spring constant s Complex frequency (Laplace variable) t Time x Input function (time domain) u Base displacement coordinate z Relative displacement coordinate A Amplitude H Frequency response function 11.1 Introduction Accelerometers are ubiquitous for measurements of structural dynamics and other dynamic events. Several types of transduction mechanisms can be used for sensing acceleration; piezoelectric, capacitive, and servo (or force balance) [1] are all common classes of accelerometers. Piezoresistive (PR) sensors have long been used in high shock environments [2] and are desirable in these applications for two primary reasons. First, piezoelectric elements have been shown to be susceptible to domain depoling in extreme shock events [3]. PR microelectromechanical systems (MEMS) are also readily manufactured from silicon dies using conventional electronic machining processes. J.R. Foley ( ) • T.J. Lagoski • J. Brown Air Force Research Laboratory, AFRL/RWMF, 306 W. Eglin Blvd., Bldg. 432, Eglin AFB, FL 32542-5430, USA e-mail: jason.foley.1@us.af.mil J. Hong Applied Research Associates, Inc., 956 W. John Sims Pkwy., Niceville, FL 32578, USA © The Society for Experimental Mechanics, Inc. 2015 A. Wicks (ed.), Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15233-2_11 105
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